Quantifying free energy profiles of proton transfer reactions in solution and proteins by using a diabatic FDFT mapping.

Reliable studies of proton transfer (PT) reactions in solution and in enzymes by combined quantum mechanical/molecular mechanics (QM/MM) approaches with an ab initio description of the quantum region present a major challenge to computational chemists. The main problem is the need for extensive computer time to evaluate the QM energy, which in turn makes it extremely challenging to perform proper configurational sampling. The present work presents a new effective way for performing such calculations by using the frozen density functional (FDFT) approach to generate diabatic surfaces that are used to generate a mapping potential that takes the system from the reactant to the product state. The resulting umbrella sampling/free energy perturbation (US/FEP) mapping is done in full analogy with the approach used in the empirical valence bond (EVB) treatment, moving from the diabatic mapping potential to the adiabatic ground state surface, while an ab initio Hamiltonian is used for the QM part. The present approach provides a particularly effective way for evaluating the free energy associated with both the substrate and the solvent motions. This allows us to obtain a free energy barrier that properly reflects the solute entropy. This advance allows one to obtain ab initio QM/MM (QM(ai)/MM) free energy surfaces for very challenging cases such as the autodissociation of water in water, proton transfer between methanol and water in water, and the effect of Mg2+ ion on such a reaction. We also consider as a benchmark the initial PT reaction in the catalytic cycle of triose phosphate isomerase and obtain excellent results without any adjustable parameters. Our results point out that the present implementation of the FDFT approach provides a very promising approach for evaluating QM(ai)/MM free energy surfaces.